{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:C6NGFIIV3YGJAHQZHKWSFRDOEL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"313d0d76fc663b41765eef9be3cff78bb9875ac5fbf8a0be7d7623474c8b03da","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-31T13:39:21Z","title_canon_sha256":"1850b5534db71f45ab423624f479b2c5ae6f94d9ed807370f8423594e801b7d8"},"schema_version":"1.0","source":{"id":"1105.6275","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.6275","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1105.6275v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.6275","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"C6NGFIIV3YGJ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"C6NGFIIV3YGJAHQZ","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"C6NGFIIV","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:042a9151f64b3f7c803cf029661e56eb5e95c48cb57bd3e60cd32f1d0b546c53","target":"graph","created_at":"2026-05-17T23:53:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the behaviour of a Hilbert geometry when going to infinity along a geodesic line. We prove that all the information is contained in the shape of the boundary at the endpoint of this geodesic line and have to introduce a regularity property of convex functions to make this link precise. The point of view is a dynamical one and the main interest of this article is in Lyapunov exponents of the geodesic flow.","authors_text":"Micka\\\"el Crampon (IRMA)","cross_cats":["math.DG","math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-31T13:39:21Z","title":"Lyapunov exponents in Hilbert geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.6275","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:10fb3be9f29ca3c6d29785c3ee9ab3d0fa305299cea62db7c500a379f4efd98c","target":"record","created_at":"2026-05-17T23:53:36Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"313d0d76fc663b41765eef9be3cff78bb9875ac5fbf8a0be7d7623474c8b03da","cross_cats_sorted":["math.DG","math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-05-31T13:39:21Z","title_canon_sha256":"1850b5534db71f45ab423624f479b2c5ae6f94d9ed807370f8423594e801b7d8"},"schema_version":"1.0","source":{"id":"1105.6275","kind":"arxiv","version":1}},"canonical_sha256":"179a62a115de0c901e193aad22c46e22f7925e3a6af823eb04b19b0c3e2d96cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"179a62a115de0c901e193aad22c46e22f7925e3a6af823eb04b19b0c3e2d96cc","first_computed_at":"2026-05-17T23:53:36.580590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.580590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lQpv3GM5AnXXpipEwJ4EPP88ZyZr60x79tFHsT+DPwplCyzuyoogvY755gzjLQsY+EYh8Q/LtYcR5eGVZmikBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.581364Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.6275","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:10fb3be9f29ca3c6d29785c3ee9ab3d0fa305299cea62db7c500a379f4efd98c","sha256:042a9151f64b3f7c803cf029661e56eb5e95c48cb57bd3e60cd32f1d0b546c53"],"state_sha256":"d4f943c8c4d5b966b551c489bd7aadca378895115132b33e6aa796b3e206e539"}